Convolution Definition and 364 Threads

Hello, Consider I have a linear time-invariant (LTI) system, with ##x(t)##, ##y(t)##, and ##h(t)##, as input, output, and impulse response functions, respectively. I have two choices to write the convolution integral to get ##y(t)##: $$ 1)\ \ \ y(t) = \int_{0}^{t} h(t-t')x(t')dt' $$ and...

How would you interpretate this image about LTI systems and convolution?

1. First of all, a block diagram is given where x(t) is the input and y(t) the output.The y(t) is asked when given the h(t) and x(t).We have in parallel h(t) and δ(t-1)*h(t) and those 2 go through a summer (the second one with minus and the first one with a plus) and give y(t). 2. I know from...

Evaluate the following discrete-time convolution: y[n] = cos(\frac{1}{2}\pin)*2^{n}u[-n+2] Here is my sloppy attempt: y[n] = \sumcos(\frac{1}{2}\pik)2^{n-k}u[-n-k+2] from k = -∞ to ∞ = \sumcos(\frac{1}{2}\pik)2^{n-k} from k = -∞ to 2 We can re-write the cos as...

Hello all, I am having some trouble calculating a convolution. For the question, and my attempt at a solution, please take a look at the pic. Can someone please point me in the right direction?

Boas Ch. 8, Sec. 10 #3 Use the convolution integral to find the inverse transforms of: \frac{p}{(p^{2}-1)^{2}} = \frac{p}{p^{2}-1} \frac{1}{p^{2}-1} I'm completely confused with these things. Are we supposed to figure out the inverse Laplace transform and then use that within our convolution...

I have given the question and my attempt in the image that i have loaded please tell me that am i doing it right ?

Hi PF, What is circular convolution? Why do we need such an operation if we have linear convolution, What is its basic difference of both convolutions. Is circular convolution used only in frequency domain? -Devanand T

Homework Statement Compute the convolution y[n] = x[n] * h[n] if discrete signals: x[n] = \alpha^nu[n] h[n] = \beta^nu[n] Where \alpha \neq \beta. Homework Equations y[n] = \sum_{k=-\infty}^{\infty} h[n-k]x[k] The Attempt at a Solution I plugged the two equations into...

Hello all. I have a homework question but since I have no idea how to go about solving it I have started with an exercise problem from the book (with the solution and vague steps provided). Here is my attempt of the exersize question. Homework Statement Compute the convolution y[n] = x[n]...

Okay, so this is the first time I'm encountering this theorem and I'm not very strong in calculus. But I tried to understand it myself but couldn't. Convolution theorem is the one in the attachment as give in the book ( couldn't find a way to type that out easily). My doubt is if laplace(f)...

I am trying to prove the convolution of the Fourier Transform $$ (\widehat{f\star g})(\xi) = 2\pi\hat{f}(\xi)\hat{g}(\xi) $$

Homework Statement Find the Fourier transform of the following signal JUST by using the FT table and the FT properties x(t) = sin(t) -pi<=t<=pi 0 otherwise NOTE: I am using CONVOLVED WITH as a substitute for * (the real convolution operator) because I cannot express...

Homework Statement Consider an LTI system with impulse response h(t) = (0.5sin(2t)/(t) Find system output y(t) if x(t) = cos(t) + sin(3t) Homework Equations y(t) = x(t)*h(t) The Attempt at a Solution I am only familiar with doing much simpler convolutions using graphical...

Homework Statement Find the inverse laplace transform of (2/(s+2)^4) using the given table of identities: Homework Equations Here are the given identities: The Attempt at a Solution Alright, I realize that there is a simple identity that I can use with a factorial symbol, but this...

Homework Statement tx'' + (4t-2)x' + (13t-4)x = 0 Use laplace transform to solve. The Attempt at a Solution I've split up the X'(s) and X(s) and integrated to get X(s) = \frac{c}{(s^2 + 4s + 13)^2} = \frac{c}{9} \left[ \frac{3}{(s+2)^2 + 9} \right]^2 From this I'm guessing...

Hello, I consider two functions f:R^2 \rightarrow R and g:R^2 \rightarrow R, and the two dimensional convolution (f \ast g)(\mathbf{x}) = \int_{\mathbb{R}^2}f(\mathbf{t})g(\mathbf{x-t})d^2\mathbf{t} I proved using the Fourier transform and the convolution theorem that the convolution of two...

I've been trying to code an algorithm to compute the convolution of two probability distributions. using the FFT. This relies on the "convolution theorem": (p*q)[z] = FFT^{-1}(FFT(p) \cdot FFT(q)) However, when I test it using the distributions p={0.1, 0.2, 0.3, 0.4} q={0.4, 0.3, 0.2, 0.1}...

So here is my problem: Find the output y(t) given the input x(t) and the input response h(t). x(t) = e-tu(t) h(t) = u(t-2)-u(t-4) Relevant equations: y(t) = x(t)*h(t) = ∫e-\tau u( \tau )(u(t-\tau-2)-u(t-\tau-4))d\tau What I don't get: How do I write h(t) in the integral? I think I'm just...

Is this true: h(t)* Heaviside(t-t0) = h(t0) If this is true saves my work a lot. It appears not to be true I tried proving it...

Homework Statement Homework Equations The Attempt at a Solution See the 2 figures attached below. Am I doing this correctly? Is the result I obtained correct? Is there a easier way I could've solved this problem? Thanks again!

Homework Statement Convolve, 2e^{-t}u(t) \ast e^{t}u(-t) \quad \text{Where u(t) is the step function} Homework Equations The Attempt at a Solution 2e^{t}\int_{?}^{?}e^{-\tau}u(\tau) e^{-\tau}u(-t+\tau)d \tau I'm not sure what the limits on my integral should be, the u(-t) is confusing me...

I'm really confused about the idea of convolution and could really use some help understanding it. Wikipedia says: Emphasis added. It seems to me that since the two functions are being multiplied together and then integrated that the integral should give the product of the areas of the...

A while back I tended a course in transform methods. During the course we were handed a MAtlab program that could be used to simulate convotution called Discrete Convolution Demo. It's kind of big or you might say bloated and I'd like some lightweight version or something. If someone know some...

Hi there, working on a physical problem I found two functions that should be equivalent, and indeed they seem to be after a numerical check. The functions are shown in the attached PDF. I can not figure a way to prove their equivalence analytically (the double integral especially gives me...

Hello there, I am really struggling to prove that "The integral of the convolution between functions f and gequals the product of their integrals", http://en.wikipedia.org/wiki/Convolution#Integration Can anybody give me a hint? Many thanks

Hi, I need help about the convolution of 3 functions as shown in attached file via FFT. Specially I need help about the Matlab implementation of whole process. Thanks in Advance. Regards Kamru

Hi, I want to verify that the form of a particular solution satisfies the following ODE: v' + (b/m)v = u/m with vpart= ∫e-(b/m)(t-r) (u(r)/m) dr where the limits are from 0 to t So I tried to differentiate v with respect to t, in order to substitute it back into the equation. But, how do...

Hi, I am doing research and I am stuck at this point I need help to convolute iid non central chi-square with normal distribution.

This was the bonus question on my test, I couldn't really figure out how to begin.

hello Does "quartus" have any special function or module for calculating discrete-time convolution?

Thanks to those who participated in last week's POTW! Here's this week's problem. ----- Problem: Recall that the convolution of $f$ and $g$ is defined by the integral \[(f\ast g)(t) = \int_0^{t}f(t-\tau)g(\tau)\,d\tau.\] Establish the commutative, distributive, and associative properties of...

Homework Statement Find the convolution of g(x) = e^{-πx^{2}} with itself from -∞ to ∞ using the definition of convolution, not the Fourier Transform. The Attempt at a Solution See my attachment. My professor said that you have to use integration by parts, but I keep getting stuck...

Hi I have the following piece of code: dataX = -4:1:4; dataY = [0 -1 -10 -40 -55 10 40 10 1]; figure(1) plot(dataX, dataY, '*'); x = -2:0.01:2; plot(-4:0.01:4, 1*conv(exp(-x).*heaviside(x),sin(x)), dataX, dataY, '*') mdl = @(a, x)(a(1)*conv(exp(-x).*heaviside(x),sin(x)))...

Hi I have the following code: lorentz[A_, Ox_, Oy_, FWHM_, x_] := A (1/3.14) FWHM/((x - Ox)^2 + FWHM^2) + Oy; gauss[A_, Ox_, Oy_, x_, C_] := A Exp[-(x - Ox)^2 C] + Oy; Convolve[lorentz[1, 0, 0, 1, x], gauss[1, 0, 0, x, 1], x, y] It takes extremely long time for this to finish -- is it...

I've arrived at the following equation involving the convolution of two functions: f(x) = \int_{-\infty}^{\infty} f(t) g(t-x) dt = f(x) \ast g(x) Where: g(z) = e^{-z^2/2} In other words, a function convoluted with a Gaussian pdf results in the same function. I've tried taking Fourier...

Hello there, I can not work out a computation i found, involving the convolution of a convolution. G is a function, as well as ε, and using the notation G*ε = ∫G(t-tau) dε (the integral being performed between 0 and t) I want to compute G*ε*ε I try (G*ε)*ε and end up with...

Dear friends, I am interesting to find some functions g satisfying the following convolution inequality (g\astv)(t)\leqv(t) for any positive function v\inL^{1}[0,T] and * denotes the convolution between g and v.

hi I really need your help ... for linear time invariant system f(t) =f1(t) (convolution) f2(t) f(t) = ∫f1(t).f2 ( t-T) or f(t) = ∫f1(t-T).f2(t) where f1(t) = delta function = δ(t).δ(t-2) and f2(t) = sine wave = sin ( ∏t ) how i can solve this ... my problem is : how can i...

Ok, I know the Fourier effect of a time shift is a multiplication with an exponential: x(t-t0) → exp(-j2∏f*t0)X(f) Now say Y(f) is the Fourier transform of y(t). What I am wondering what is the difference in the Fourier space when convolving Y(f) with either X(f) or exp(-j2∏f*t0)X(f)...

I am trying to see if I understand the convolution process correctly. This is from the solved example of my prof's notes: x[n] = u[n] and h[n] = a-nu[-n] for 0<a<1 As expected the first step was y[n] = x[n]* h[n] = Ʃ h[k]x[n-k] -∞<k<∞ = Ʃ a-ku[-k]u[n-k] -∞<k<∞ From my...

Homework Statement Let y(t) be the convolution of x(t) with h(t), show that the area under y(t) is the product of the areas under x(t) and h(t) Homework Equations Convolution definition The Attempt at a Solution I found a derivation but it skips a step, uploaded it here: htt...

Greetings, We just had 1.5 classes about this topic (due to some unavoidable circumstances in our country...) so our teacher just scribbled and roughly explained them on the board...So after i got home i couldn't get some steps he did for convolution in z-transform: find inverse z-transform...

Homework Statement This is a question from a sample exam, rather than a homework problem. \text{Let }f \text{ be the periodic function with period } 1 \text{ defined for }-1/2\leq t<1/2 \text{ by }f(t)=t^2\\ \text{ and let }g \text{ be the periodic function with period } 1 \text{ defined...

Homework Statement How do you do a convolution of two functions containing only impulses? Homework Equations Say you have 2 functions to convolve, f1 and f2. I can't do the impulse symbol, so let's call it q. Say f1 = 2q(t+1) + 2q(t-4) and f2 = q(t-3) What is f1 convolved with f2? Or how...

Homework Statement http://gyazo.com/22f5c655071e49adf3f4652e8042873b I derived the proof myself, but by arbitrary changing the t limit to infinity. I'm hoping that by understanding the diagram in the link above I will have a better idea of why I changed the limit. I currently look at it...

Hi all, I am trying figure out this diffraction problem. I have to find the intensity distribution of a four slit fraunhofer diffraction grating using the convolution theorem. I can do the math and all...but I do not know how to start it! The only information I am given is the slits have...

Hi, I have a quick question about certain algebraic properties of convolution. If I have 3 functions x(f), y(f) and z(f), is the following true? [x(f) . g(f)] * z(f) = [x(f) * z(f)].g(f) I looked on Wikipedia but there's only a property like this if one of the terms is a scalar, so most...

Determine the confolution of f with itself where f is: f(t) = 1 for ltl<1 and 0 everywhere else Then deduce that: ∫-∞∞ sin2ω/ω2 dω = ∏ Fouriertransform of f gives: f(ω) = 2/√(2∏) sin(ω)/ω and using the convolution theorem gives: f*f = 4/√(2∏) sin2(ω)/ω2 But I'm clueless...

Hey! So when I enter this in Mathematica In[246] = ZTransform[Sum[f[k] g[k - n], {k, 0, n}], n, z] InverseZTransform[%, z, n] I get: Out[246] = ZTransform[f[n], n, z] ZTransform[g[-n], n, z] Out[247] = InverseZTransform[ZTransform[f[n], n, z] ZTransform[g[-n], n, z], z, n]...